1. ## Probability

I need help with the following question please.
A box contains 5 balls, marked with numbers 1 to 5. A playerwithdraws at random two balls from the box and is to receive an amount indollars equal to the product of the two numbers marked on the balls. Calculatethe expected value and variance of the amount the player will receive.

2. ## Re: Probability

Originally Posted by mlg
A box contains 5 balls, marked with numbers 1 to 5. A player withdraws at random two balls from the box and is to receive an amount indollars equal to the product of the two numbers marked on the balls. Calculatethe expected value and variance of the amount the player will receive.
There are ten ways to draw two balls from the box. The outcome sum can be any integer from 3 to 9.
Show us some work on your part.

4. ## Re: Probability

The two balls can be 12,13,14,15,23,24,25,34,35,45.
As the question mentions product of the two numbers, should this mean that that the outcome product range from 2(1x2) to 20(4x5)?

5. ## Re: Probability

Originally Posted by mlg
The two balls can be 12,13,14,15,23,24,25,34,35,45.
As the question mentions product of the two numbers, should this mean that that the outcome product range from 2(1x2) to 20(4x5)?
You are correct, I read "sum" where it says "product".
Note that each of those ten products occurs in only one way $\mathcal{P}(25)=\dfrac{1}{10}$.

To find the expected value take the sum of the outcomes times the the probability of the outcome.

6. ## Re: Probability

Thanks again.